Variation of Geomagnetic Index Empirical Distribution and Burst Statistics Across Successive Solar Cycles

The overall level of solar activity, and space weather response at Earth, varies within and between successive solar cycles and can be characterized by the statistics of bursts, i.e., time series excursions above a threshold. We consider nonoverlapping 1‐year samples of the auroral electrojet index (AE) and the SuperMAG‐based ring current index (SMR), across the last four solar cycles. These indices, respectively, characterize high latitude and equatorial geomagnetic disturbances. We suggest that average burst duration τ̄ $\bar{\tau }$ and burst return period R̄ $\bar{R}$ form an activity parameter, τ̄/R̄ $\bar{\tau }/\bar{R}$ which characterizes the fraction of time the magnetosphere spends, on average, in an active state for a given burst threshold. If the burst threshold takes a fixed value, τ̄/R̄ $\bar{\tau }/\bar{R}$ for SMR tracks sunspot number, while τ̄/R̄ $\bar{\tau }/\bar{R}$ for AE peaks in the solar cycle declining phase. Level crossing theory directly relates τ̄/R̄ $\bar{\tau }/\bar{R}$ to the observed index value cumulative distribution function (cdf). For burst thresholds at fixed quantiles, we find that the probability density functions of τ and R each collapse onto single empirical curves for AE at solar cycle minimum, maximum, and declining phase and for (−)SMR at solar maximum. Moreover, underlying empirical cdf tails of observed index values collapse onto common functional forms specific to each index and cycle phase when normalized to their first two moments. Together, these results offer operational support to quantifying space weather risk which requires understanding how return periods of events of a given size vary with solar cycle strength. Plain Language Summary Earth's magnetosphere and ionosphere have their own space weather. Space weather storms can cause technological problems including electrical grid damage and satellite system disruption. The overall driving of space weather follows the solar cycle of activity which has a period of approximately 11‐years. Geomagnetic indices, based on magnetic field observations at the Earth's surface, provide almost continuous monitoring of magnetospheric and ionospheric activity. We analyze two geomagnetic index time series, AE and SMR, which track activity in the auroral region and around the Earth's equator, respectively. We identify bursts or excursions above thresholds in the AE and SMR time series. We find that the ratio of average burst duration to return period provides a useful a